Abstract
We use methods of real analysis to continue the Riemann zeta function $\zeta(s)$ to all complex $s$, and to express the values at integers in terms of Bernoulli numbers, using only those infinite series for which we could write down an explicit estimate for the remainder after $N$ terms. This paper is self-contained, apart from appeals to the uniqueness theorems for analytic continuation and for real power series, and, verbis in Latinam translatis, would be accessible to Euler.
Citation
Martin N. Huxley. "A short account of the values of the zeta function at integers." Funct. Approx. Comment. Math. 58 (2) 245 - 256, June 2018. https://doi.org/10.7169/facm/1701
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